Change in the adiabatic invariant at a separatrix crossing in a nonlinear two-mode model of Feshbach resonance.

Alexei Vasiliev, Alexander Itin

Mean-field approach has recently been used to model coupled atom-molecular Bose-Einstein condensates (BEC)and coupled Fermi-Bose condensates near Feshbach resonance. Sweeping of magnetic field across the resonance corresponds to a separatrix crossing in a Hamiltonian system with one d.o.f. depending on a slowly varying parameter. We calculate change in the adiabatic invariant (action) at the separatrix crossing, which corresponds to finite-rate efficiency of the sweep.